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<H3>improper_style ring command 
</H3>
<H3>improper_style ring/omp command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>improper_style ring 
</PRE>
<P><B>Examples:</B>
</P>
<PRE>improper_style ring
improper_coeff 1 8000 70.5 
</PRE>
<P><B>Description:</B>
</P>
<P>The <I>ring</I> improper style uses the potential
</P>
<CENTER><IMG SRC = "Eqs/improper_ring.jpg">
</CENTER>
<P>where K is a prefactor, theta is the angle formed by the atoms
specified by (i,j,k,l) indices and theta0 its equilibrium value.
</P>
<P>If the 4 atoms in an improper quadruplet (listed in the data file read
by the <A HREF = "read_data.html">read_data</A> command) are ordered i,j,k,l then
theta_<I>ijl</I> is the angle between atoms i,j and l, theta_<I>ijk</I> is the
angle between atoms i,j and k, theta_<I>kjl</I> is the angle between atoms
j,k, and l.
</P>
<P>The "ring" improper style implements the improper potential introduced
by Destree et al., in Equation (9) of <A HREF = "#Destree">(Destree)</A>.  This
potential does not affect small amplitude vibrations but is used in an
ad-hoc way to prevent the onset of accidentially large amplitude
fluctuations leading to the occurrence of a planar conformation of the
three bonds i-j, j-k and j-l, an intermediate conformation toward the
chiral inversion of a methine carbon.  In the "Impropers" section of
data file four atoms: i, j, k and l are specified with i,j and l lying
on the backbone of the chain and k specifying the chirality of j.
</P>
<P>The following coefficients must be defined for each improper type via
the <A HREF = "improper_coeff.html">improper_coeff</A> command as in the example
above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands:
</P>
<UL><LI>K (energy/radian^2)
<LI>theta0 (degrees) 
</UL>
<P>theta0 is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian^2.
</P>
<HR>

<P>Styles with a <I>cuda</I>, <I>gpu</I>, <I>omp</I>, or <I>opt</I> suffix are functionally
the same as the corresponding style without the suffix.  They have
been optimized to run faster, depending on your available hardware, as
discussed in <A HREF = "Section_accelerate.html">Section_accelerate</A> of the
manual.  The accelerated styles take the same arguments and should
produce the same results, except for round-off and precision issues.
</P>
<P>These accelerated styles are part of the USER-CUDA, GPU, USER-OMP and OPT
packages, respectively.  They are only enabled if LAMMPS was built with
those packages.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
section for more info.
</P>
<P>You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the <A HREF = "Section_start.html#start_7">-suffix command-line
switch</A> when you invoke LAMMPS, or you can
use the <A HREF = "suffix.html">suffix</A> command in your input script.
</P>
<P>See <A HREF = "Section_accelerate.html">Section_accelerate</A> of the manual for
more instructions on how to use the accelerated styles effectively.
</P>
<HR>

<P><B>Restrictions:</B>
</P>
<P>This improper style can only be used if LAMMPS was built with the
USER-MISC package.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
section for more info on packages.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "improper_coeff.html">improper_coeff</A>
</P>
<A NAME = "Destree"></A>

<P><B>(Destree)</B> M. Destree, F. Laupretre, A. Lyulin, and J.-P.  Ryckaert,
J Chem Phys, 112, 9632 (2000).
</P>
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